A natural question is whether inversity captures the same information (with opposite sign) as degree assortativity, which is a well known network property \(\rho _a=Corr\left(D^{\mathbf {O}},D^{\mathbf {D}}\right)\)  capturing the correlation in degree across all edges in the network [1]}, [2]}, [3]}. To examine this question, we generate \(1,000\)  networks using different generative methods as above. We find that assortativity and inversity are not guaranteed to have opposite signs (Fig. A). Therefore, the sign of assortativity cannot be used to determine whether the local or global mean is greater for a network, unlike with inversity. All 3 network generating processes create networks with the same sign for both metrics (detail in Fig. B). Example networks for the case of same sign assortativity and inversity are illustrated (Fig. C, D), showing that it is not obvious to predict inversity of a network if we know its assortativity.
